Statistical inference for stationary linear models with tapered data

Abstract

: In this paper, we survey some recent results on statistical infer- ence (parametric and nonparametric statistical estimation, hypotheses testing) about the spectrum of stationary models with tapered data. We also discuss some questions concerning tapered Toeplitz matrices and operators, central limit theorems for tapered Toeplitz type quadratic functionals, and tapered Fej´er-type kernels and singular integrals. These are the main tools for obtaining the corresponding results, and also are of interest in them- selves. The processes considered will be discrete-time and continuous-time Gaussian, linear or L´evy-driven linear processes with memory.